Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Self-Dual Maxwell Fields from Clifford Analysis
View through CrossRef
Abstract
The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions. In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for the Spacetime Algebra Cl(3, 1) these equations are the equations for a self-dual source free Maxwell field, and for a massless uncharged Spinor. This shows a deep link between fundamental physics and the Clifford geometry of Spacetime.
Title: Self-Dual Maxwell Fields from Clifford Analysis
Description:
Abstract
The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations.
The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions.
In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for the Spacetime Algebra Cl(3, 1) these equations are the equations for a self-dual source free Maxwell field, and for a massless uncharged Spinor.
This shows a deep link between fundamental physics and the Clifford geometry of Spacetime.
Related Results
Anne Clifford
Anne Clifford
Lady Anne Clifford (b. 30 January 1590–d. 22 March 1676) spent a considerable portion of her life embroiled in lawsuits attempting to recover her father’s extensive land holdings a...
Efficient Unitary Designs with a System-Size Independent Number of Non-Clifford Gates
Efficient Unitary Designs with a System-Size Independent Number of Non-Clifford Gates
AbstractMany quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the fu...
SELF-ESTEEM AND SELF-EFFICACY AMONG NEWSCASTERS AND NEWS REPORTERS
SELF-ESTEEM AND SELF-EFFICACY AMONG NEWSCASTERS AND NEWS REPORTERS
The present study aimedto investigaterelationship between self-esteem and self-efficacy among news casters and news reporters and to compare both groups in self-esteemand self-effi...
Brownian Motion, Martingales and Itô Formula in Clifford Analysis
Brownian Motion, Martingales and Itô Formula in Clifford Analysis
AbstractClifford analysis has been the field of active research for several decades resulting in various methods to solve problems in pure and applied mathematics. However, the are...
The Automedial Zaniness of Ryan Trecartin
The Automedial Zaniness of Ryan Trecartin
IntroductionThe American artist Ryan Trecartin makes digital videos that centre on the self-presentations common to video-sharing sites such as YouTube. Named by New Yorker critic ...
Design and analysis of dual-curing systems
Design and analysis of dual-curing systems
Dual-curing processing is a method to prepare thermoset materials through two polymerization reactions carried out
simultaneously or sequentially. In these processes, a firm under...
Helmholtz Hamiltonian Mechanics Electromagnetic Physics Gaging Generalizing Mass-Charge and Charge-Fields Gage Metrics to Quantum Relativity Gage Metrics
Helmholtz Hamiltonian Mechanics Electromagnetic Physics Gaging Generalizing Mass-Charge and Charge-Fields Gage Metrics to Quantum Relativity Gage Metrics
This article will continue ansatz gage matrix of Iyer Markoulakis Helmholtz Hamiltonian mechanics points’ fields gage to Pauli Dirac monopole particle fields ansatz gage ...
Clifford Dobell 1886-1949
Clifford Dobell 1886-1949
Abstract
The sudden and premature death of Clifford Dobell on 23 December 1949, in London, deprived the scientific world of one of the outstanding protozoologists...